[cafard]

But isn't Beppe an Italian nickname for Giuseppe?

[eesmith]

I'm way out of my depth, and it appears to be full of folk etymology.

http://spanishlinguist.us/2013/03/pepe-and-paco-2-mysterious... says Real Academia España says Pepe comes from Beppe and there is no support for the "pater comunitatis" origin for Paco.

There is much discussion in the comments.

[borroka]

"Beppe" and the less used "Beppo" are both diminutives (not nicknames) of the popular (especially back in the day) biblical name Giuseppe. "Chicco" is an interesting case in Italian, as it is more of a nickname than a diminutive (hypocoristic, to be precise), and it can be used for the full names Francesco, Enrico, or Federico.